We now ask how appropriate is the Hylleraas-Majorana solution in \(d-\) dimensions for
the study of He-like ions and, in general, of three-body Coulomb systems. Recently [1]}, [2]} several aspects of a general quantum three-body system in \(d\) -dimensions \((d>1)\)  with arbitrary masses have been reported (see also [3]}). Needless to
say, the \(d-\) dimensional He atom has been analyzed in some detail by several authors [4]}-[5]} mainly within the infinite nuclear mass approximation. Again, all these treatments require of elaborate theoretical and numerical procedures which make it difficult to follow a clear physical picture of the role of the relevant parameters involved. Hence, it is desirable to search for compact –yet reasonably accurate– physical ground state wavefunctions in \(d\) -dimensions for these systems. This is the main focus of this work as explained below.
